# Properties

 Label 303450.x Number of curves $2$ Conductor $303450$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 303450.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.x1 303450x2 $$[1, 1, 0, -8294450, -54402943500]$$ $$-6693187811305/131714173248$$ $$-1241898416035763325000000$$ $$[]$$ $$55987200$$ $$3.3042$$
303450.x2 303450x1 $$[1, 1, 0, 917425, 1964519625]$$ $$9056932295/181997172$$ $$-1716003631622995312500$$ $$[]$$ $$18662400$$ $$2.7549$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 303450.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 303450.x do not have complex multiplication.

## Modular form 303450.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 6q^{11} - q^{12} - 4q^{13} + q^{14} + q^{16} - q^{18} - q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 